Acoustic interrogation of subsurface features tends to be limited by the size and power of practical sources, and in practice, the output of downhole acoustic transducers is limited by the power transmission capabilities of the wire line cable. High frequency signals have a relatively short penetration distance, while low frequency signals generally require large sources, clamped to the borehole wall, to maximize energy transfer to the formation and minimize unwanted signals within the well bore. It is difficult to generate a collimated acoustic beam signal in the 10 kHz-100 kHz range from the borehole to probe the rock formation surrounding a borehole, or any other material in the environment, such as casing or cement, with conventional low-frequency transducers. Conventional low-frequency acoustic sources in this frequency range have low bandwidth, less than 30% of the center frequency, and very large beam spread that depends on the frequency, such that as the frequency decreases, the beam spread increases. The generation of a collimated beam requires a number of conditions to be satisfied, including a long source array, uniform coupling of all the transducers to the rock formation around the borehole and knowledge of the acoustic velocities of the rock formation. In the borehole environment, these conditions are not often achievable because of underlying physics constraints, engineering feasibility or operating conditions.
Acoustic beam sources based on a non-linear mixing of acoustic waves have been proposed for general applications in fluid media, such as underwater sonar, since the 1950s. For subsurface applications, U.S. Pat. No. 3,974,476 to Cowles discloses an acoustic source for borehole surveys. The disclosure of Cowles describes an acoustic source generation device, for example, a device that is capable of the generation of a 1 kHz frequency beam by mixing two frequencies around 5 MHz in a borehole environment violates basic physical principles. A typical wireline logging tool has a diameter of 3⅝ inch (9.2 cm), while the wavelength of a 1 kHz wave in a typical fluid of 1500 m/s is 1.5 m. This represents close to 10 times the borehole diameter. This 1 kHz acoustic wave cannot stay collimated without violating the basic uncertainty principle of wave diffraction physics. Moreover, the mixing of 5 MHz frequencies to generate a 1 kHz wave represents a step-down frequency ratio of 5000:1, which has not been demonstrated to be achievable in practice.